Question

Lily has $2.75 in her pocket, consisting of dimes and quarters. If there are 17 coins in all, how many of each does she have?

Answer 1

Lily has 10 dimes and 7 quarters

Explanation:

Let x be the number of dimes and y be the number of quarters Lily has in her pocket.

If there are 17 coins in all, then

`x+y=17`

The amount in dimes is 10x cents, the amount in quarters is 25y cents. Lily has $2.75 = 275 cents in her pocket, then

`10x+25y=275`

From the first equation,

`x=17-y`

Substitute it into the second equation:

`10(17-y)+25y=275\\ \\170-10y+25y=275\\ \\25y-10y=275-170\\ \\15y=105\\ \\y=7\\ \\x=17-y=17-7=10`

Lily has 10 dimes and 7 quarters